Supported by CNCS-UEFISCDI contract no 194/2017, hosted by Horia Hulubei National Institute for Physics and Nuclear Engineering, Bucharest.


The discovery of the fission process and its explanation was one of the most important advances in nuclear physics of the last century. It was not only important for the fundamental understanding of heavy nuclei but also for the applications. The prompt fission neutrons (PFN) are mandatory in producing nuclear energy since they make the chain reaction of fissile nuclei possible. Their properties are essential for the design of nuclear power plants, the safe operation of nuclear reactors, the handling of nuclear waste and the investigation of next-generation reactor systems and fuel cycles.

A detailed theoretical study of PFN properties is therefore of utmost importance and this is the context in which the present project takes place. The main characteristics of the PFN (an emission along the fission axis and an exponentially decreasing energy spectrum) led to the first guess about their origin: they are evaporated by the fission fragments when these fragments are fully accelerated. The emission is supposed to occur relatively long after the division of the fissioning system into two fragments.

However, some observed PFN characteristics suggest the existence of an earlier (e.g. around scission) neutron emission of a different origin. This is due to the rapidly changing neutron-nucleus potential during the scission process.

The goal of this project is to provide elements for answering the important question of the nature and relative abundance of the two components of the prompt fission neutrons (emitted during scission and evaporated from accelerated fragments).

A recent dynamical scission model will be used to calculate the characteristics of the neutrons dynamically released during the scission process, i.e., during the rupture of the neck connecting the nascent fragments and the absorption of the neck stubs by the primary fragments. Three categories of observables will be tackled:

1) The scission neutron multiplicity. Its dependence on the fragments' mass ratio and on the model assumptions will be studied.

2) The angular distribution of the scission neutrons with respect to the fission axis. Its dependence on the mass ratio, on the projection of the angular momentum on the nuclear axis and on the fragments' deformation at scission will be investigated.

3) The scission neutron energy spectrum. Its shape and its average value will be studied as a function of the mass asymmetry and of the model assumptions. Additional information on the time evolution of the emission process will be obtained by calculating the time dependent decay rate.

The old hypothesis that fission neutrons are evaporated from fully accelerated fragments will be also investigated. For this we will employ an advanced version of the Hauser-Feshbach statistical approach combined with a Monte-Carlo sampling of initial conditions. The same observables will be estimated with both methods and the results compared. When possible, the two models will be confronted with experimental data.

REPORT 2017 (in English)

REPORT 2018 (in English)

REPORT 2019 (in English)




[1] Parallel theoretical study of the two components of the prompt fission neutrons: dynamically released

at scission and evaporated from fully accelerated fragments, N.Carjan, M.Rizea, P.Talou, EPJ Web of Conferences 146,, p.1-6 (2017)

[2] Fourier transform of single-particle wave functions in extremely deformed nuclei: towards the momentum distribution of scission neutrons, M.Rizea, N.Carjan, EPJ Web of Conferences 169, (2018)

[3] Charge polarization and the elongation of the fissioning nucleus at scission, C.Ishizuka, S.Chiba, N.Carjan, Romanian Reports in Physics 70, 202 (2018)

[4] Structures in the energy distribution of the scission neutrons: finite neutron-number effect, N.Carjan, M.Rizea, Physical Review C 99, 034613 (2019)

[5] Fission of superheavy nuclei: Fragment mass distributions and their dependence on excitation energy, N.Carjan, F.A.Ivanyuk, Yu.Ts.Oganessian, Physical Review C 99, 064606 (2019)


[1] Gross structures in the scission neutrons angular and energy distributions, N.Carjan, M.Rizea, in Theory-4: Nuclear Fission Dynamics and the Emission of Prompt Neutrons and Gamma Rays, June 20-22, 2017, Varna, Bulgaria

[2] Fourier transform of single-particle wave functions in extremely deformed nuclei: towards the momentum distribution of scission neutrons, M.Rizea, N.Carjan, in Theory-4: Nuclear Fission Dynamics and the Emission of Prompt Neutrons and Gamma Rays, June 20-22, 2017, Varna, Bulgaria

[3] Predictions of fission fragments mass distributions for super-heavy elements, N.Carjan, in Spontaneous and induced fission of very heavy and super-heavy nuclei, April 9-13, 2018, Trento, Italy and EXON-2018, IX International Symposium on Exotic Nuclei, September 10-15, 2018, Petrozavodsk, Russia

[4] Acceleration induced neutron emission in heavy nuclei, N.Carjan, M.Rizea in ISINN-26, 26thInternational Seminar on Interaction of Neutrons with Nuclei, May 28 – June 1, Xi'an, China and Fifth Joint Meeting of the Nuclear Physics Division of the American Physical Division of the American Physical Society and the Physical Society of Japan, October 23-27, 2018, Hawaii, USA

[5] Multiplicity of Scision Neutrons from Density Functional Scission Dynamics, N.Carjan, I.Stetcu, M.Rizea, A.Bulgac, in Theory-5: Nuclear Fission Dynamics and the Emission of Prompt Neutrons and Gamma Rays, September 24-26, 2019, Barga, Italy


Nicolae Carjan

Margarit Rizea


1. The shape of the scission neutrons (SN) energy spectrum

In the frame of the dynamical scission model we calculated for 236-U the distribution of the average energy of each emitted SN and compared it to the general trends of the measured spectrum. A good agreement was found. It is however necessary to calculate not only the average energy but the whole SN spectrum. For this we need to calculate the Fourier transforms of the unbound parts of the wave packets that describe the SN immediately after scission. These will provide the SN momentum distribution from which one can derive the kinetic energy distribution. It is expected that at low and high kinetic energies the SN spectrum differs from the evaporation spectrum, leading to an opportunity to distinguish between the two components of the PFN.

2. The time dependent decay rate

This calculation will reveal the time evolution of the SN emission process. It will answer questions such as: a) how long it takes before 10, 50 and 90% the neutrons released during scission leave the fissioning system and b) is the decay exponential or oscillatory? Although the two components of the PFN are separated in time, their tails may overlap. In this region a competition between scission and evaporated neutrons takes place: a possibility that has not been evoked so far.

3. Dependence of the SN energy and angular distributions on the quantum number Ω representing the projection of the angular momentum of the neutron on the symmetry (nuclear) axis

For this we will estimate the relative contribution of each set of neutron eigenstates (defined by Ω)

to these distributions. Knowing to which angular and energy domain each Ω-value contributes most, one could experimentally select PFN with more or less well defined quantum number. This possibility is unique (not available from other sources).

4. Dependence of the SN multiplicity on the mass asymmetry for 236-U and 252-Cf

The SN multiplicity will be calculated as a function of the mass ratio A-light/A-heavy and compared with total (summed over the light and the heavy fission fragments) PFN multiplicities recently measured during the rections 235-U(nth,f) and 252-Cf(sf).

5. The comparison of the results obtained with the two hypotheses about the origin of the PFN

It will be made on the mass-asymmetry dependence of the angular and kinetic energy distributions. Calculations will be made for different mass asymmetries of 236-U using both our dynamical scission model and the most advanced version of the traditional evaporation model. These predictions will be confronted with recent measurements of the same quantities.

6. The influence of the parameters of the dynamical scission model

These parameters are the neck radius of the just before scission configuration and the distance between the inner tips of the nascent fragments immediately after scission. They define the length of the non-adiabatic transition during scission. We will choose three situations that correspond to a short, an intermediate and a long jump respectively.


2017- The Fourier transform of single particle wave functions in cylindrical coordinates is applied to the study of neutrons released during scission. We propagate the neutron wave packets in time through the bi-dimensional time dependent Schrodinger equation with time dependent potential. We separate the parts of these wave packets that are in the continuum and calculate their Fourier transforms at different times: immediately after scission (T = 10^{-22} sec) and at several intervals afterwards (until T = 50 x 10^{-22} sec). The momentum distributions corresponding to these Fourier transforms are then estimated. The evolution of these distributions in time provides an insight into the separation of the neutron from the fissioning system and asymptotically gives the kinetic energy spectrum of that particular neutron.

2018- We have determined the time-dependent decay rate for the neutrons leaving a sphere around the nucleus. This provides additional informations about the evolution of the emission process. Thus, it is evaluated the time necessary for different amount of neutrons to be released from the fissioning nucleus and it is shown up the character of the scission neutron emission (exponential or oscillatory). The dependence of the decay rate on the quantum number $\Omega$ and on the radius of the sphere around the nucleus was also studied. The scission neutron angular distribution and the energy spectrum have been calculated for different time intervals and for several $\Omega$ values as well. Relevant features of the two types of neutrons (of scission and evaporated) are discussed.

2019- We have studied the dependence of the scission neutron multiplicity on the mass ratio of the fission fragments in the case of 236U and 252Cf. The multiplicities are calculated both in the sudden approximation and in the dynamical model. We have compared the results, namely the angular and the energy distribution, obtained in the frame of the two hypotheses with respect to the origin of the prompt neutrons of fission (evaporated or emitted at scission). Several tests have been performed on the influence of the dynamical model parameters: the minimal radius before scission and the distance between the interior surfaces of the fragments after scission. Comparisons with experimental data are also included.